Multiply the following complex numbers: $({-3+3i}) \cdot ({-1})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+3i}) \cdot ({-1}) = $ $ ({-3} \cdot {-1}) + ({-3} \cdot {0}i) + ({3}i \cdot {-1}) + ({3}i \cdot {0}i) $ Then simplify the terms: $ (3) + (0i) + (-3i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (0 - 3)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (0 - 3)i - 0 $ The result is simplified: $ (3 - 0) + (-3i) = 3-3i $